Emily is 3 times as old as Ashley. Twelve years ago, Emily was 7 times as old as Ashley. How old is Ashley now?
Solution: We can use the given information to write down two equations that describe the ages of Emily and Ashley. Let Emily's current age be $e$ and Ashley's current age be $a$ The information in the first sentence can be expressed in the following equation: $e = 3a$ Twelve years ago, Emily was $e - 12$ years old, and Ashley was $a - 12$ years old. The information in the second sentence can be expressed in the following equation: $e - 12 = 7(a - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $a$ , it might be easiest to use our first equation for $e$ and substitute it into our second equation. Our first equation is: $e = 3a$ . Substituting this into our second equation, we get: $3a$ $-$ $12 = 7(a - 12)$ which combines the information about $a$ from both of our original equations. Simplifying the right side of this equation, we get: $3 a - 12 = 7 a - 84$ Solving for $a$ , we get: $4 a = 72.$ $a = 18$.